Best Background for Shooting White Products

Why are you selecting GIF as the final format?

Consider two approaches to photographing the subject you described as large and white. One relates to color, and the other to lighting, and in both cases a vital consideration is crisp edge focus. Without clearly defined product edges, you are inviting trouble. 

If your choice for subject-to-surround separation is lighting, use a meter to confirm that the background white is one stop (or more) lighter than the brightest part of the product.

If your choice of subject-to-surround separation is the color of the surround, the middle gray you mentioned would work. In addition, if you use a darkish color of seamless, a major consideration is to avoid spill light -- which is a reflection of color onto to product from the background or near objects or walls.